A piece of wire of Résistance R is cut in to 5 equal parts and these

1.	A piece of wire of Résistance R is cut in to 5 equal parts and these parts are thenconnected in parallel, if the equivalent resistance of these combination is 'x' then theratio of R/x?
Answer» $\bf \underline{Given}:$ ▪ Resistance of wire: R ▪The piece of wire is cut into 5 equal PARTS. ▪If these (5 equal) parts are arranged in PARALLEL,then the equal resistance becomes x $\bf \underline{To \: find}:$ ▪ The ratio of R/x Resistance of each piece of wire after being cut into FIVE equal parts = $\sf \dfrac{R}{5} \: \Omega$ We KNOW that, in parallel combination : $\sf \implies \dfrac{1}{x} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dfrac{1}{R_4} + \dfrac{1}{R_5}$ $\sf \implies \dfrac{1}{x} = \dfrac{1}{\dfrac{R}{5} } + \dfrac{1}{\dfrac{R}{5} } + \dfrac{1}{\dfrac{R}{5} }+ \dfrac{1}{\dfrac{R}{5} }+\dfrac{1}{\dfrac{R}{5} }$ $\sf \implies \dfrac{1}{x} = \dfrac{5}{R} + \dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}$ $\sf \implies \dfrac{1}{x} = \dfrac{25}{R}$ $\sf \implies \dfrac{R}{x} = 25$ So, the ratio of R/x is 25

A piece of wire of Résistance R is cut in to 5 equal parts and these parts are thenconnected in parallel, if the equivalent resistance of these combination is 'x' then theratio of R/x?

Answer»

$\bf \underline{Given}:$

▪ Resistance of wire: R

▪The piece of wire is cut into 5 equal PARTS.

▪If these (5 equal) parts are arranged in PARALLEL,then the equal resistance becomes x

$\bf \underline{To \: find}:$

▪ The ratio of R/x

Resistance of each piece of wire after being cut into FIVE equal parts = $\sf \dfrac{R}{5} \: \Omega$

We KNOW that, in parallel combination :

$\sf \implies \dfrac{1}{x} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dfrac{1}{R_4} + \dfrac{1}{R_5}$

$\sf \implies \dfrac{1}{x} = \dfrac{1}{\dfrac{R}{5} } + \dfrac{1}{\dfrac{R}{5} } + \dfrac{1}{\dfrac{R}{5} }+ \dfrac{1}{\dfrac{R}{5} }+\dfrac{1}{\dfrac{R}{5} }$

$\sf \implies \dfrac{1}{x} = \dfrac{5}{R} + \dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}$

$\sf \implies \dfrac{1}{x} = \dfrac{25}{R}$

$\sf \implies \dfrac{R}{x} = 25$

So, the ratio of R/x is 25

A piece of wire of Résistance R is cut in to 5 equal parts and these parts are thenconnected in parallel, if the equivalent resistance of these combination is 'x' then theratio of R/x?

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